Aperiodic stabilizer for instruments on ships



July 4, 1950 w. K. H. PANOFSKY 2,514,290

APERIODIC STABILIZER FOR INSTRUMENTS ON SHIPS Filed April 20, 1944 5 Sheets-Sheet 1 INVENTOR Wolfgang ff. H. Panafa/ry y 1950 w. K. H. PANOFSKY 2,514,290

APERIODIC STABILIZER FOR INSTRUMENTS ON SHIPS Filed April 20, 1944 3 Sheets-Sheet 2 INVENTOR Wolfgang MH. Panofs/ry 3 Sheets-Sheet 3 July 4, 1950 w. K. H. PANOFSKY APERIODIC STABILIZER FOR INSTRUMENTS ON SHIPS Filed April 20, 1944 f'sky lNVENTOR Wolfgang ll. H. Pane BY l 1 ATTORKETAW Patented July 4, 1950 APERIODIC STABILIZER FOR INSTRUMENTS ON SHIPS Wolfgang K. H. Panofsky, Pasadena, Calif., assignor to the United States of America as represented by the Secretary of the Navy Application April 20, 1944, Serial No. 531,974

11 Claims. (Cl. 114191) This invention relates in general to the problem of stabilizing instruments on an unstable base Whose movement is in effect a rolling movement about a center substantially fixed with relation to the base. Although the invention ma have various other useful applications, the one I have in mind at present, and used for purposes of explanation in this description, is the stabilization of optical instruments on board ship to compensate for roll and pitch. The device of the invention is intended to compensate for the translational acceleration which is present as a component of the motion of any part of ships structure remote from its center of oscillation.

A. Assumptions of operation The operation of the stabilizer about to be described depends upon the following simplifying assumptions regarding the motion of a ship. None of these assumptions are strictly fulfilled and to the extent that they are unfulfilled, the operation of the stabilizer will depart from perfection. (1) The center of oscillation of the ship is a fixed point in relation to the ships structure.

z designed for the sole purpose of illustration and not as a definition of the limits of the invention, reference for the latter purpose z'being had to the: appended claims. 1

In the drawings: Figure 1 is a schematic view illustrating certain principles of this invention.

' Figure 2 is a diagrammatic-showing of a simple form of the apparatus of this invention.

Figure 3 is a longitudinal central section showing a typical developed form of my apparatus.

Figure 4 is a cross-section on line '44 of Fi ure 3.

Figure 5 is a cross-section on line 5-5 of Figure 3.

C. Mathematical analysis of operation The principle utilized in this device is the definite relationship between the angular acceleration of a ship and the resulting linear acceleration at a point remote from the center of oscillation.

(2) The acceleration of the center of oscillation relative to the inertial frame of reference is negligible.

B. Objects of invention It is an object of this invention to produce a device to compensate for the disturbing effect on a pendulum of the acceleration experienced by the pivot of the pendulum when that pivot is not situated at the center of oscillation of the ship, so that in spite of such acceleration of the pivot the pendulum may still hang truly vertical.

Another object of this invention is to permit a pendulum to be suspended anywhere on a ship at a point remote from the center of oscillation of the ship and insure that it will remain vertical to the same order of accuracy as it would if it were suspended at the main center of oscillation.

Another object of this invention is to provide a mechanical substitute for a servo-motor driven stabilizer controlled by a master pendulum situated at the center of oscillation of the ship.

Another object of this invention is the provision of a device which will be economical to manufacture, reliable in operation and which possesses all of the qualities of ruggedness and dependability in service. I v

Other objects and features will become apparent upon a careful consideration of the following detailed description when taken together with the accompanying drawings, the figures of which are i The method consists in coupling the pendulum mechanically to a flywheel or other body supported on the structure of the ship in neutral equilibrium in such a way that, relative to the shi when the pendulum oscillates through a: specified angle (72, the flywheel rotates in the same sense also relative to the ship through an angle different in magnitude from but proportional to a. It will be shown later that in order to minimize the moment of inertia required in the fly:

wheel, the rotation of the flywheel relative to the ship should be one half the rotation of the pendulum relative to the ship.

Figure 1 is a schematic diagram of-the device for compensating for roll around one axis only.

It is not a practical embodiment, and it is drawn as shown simply to facilitate labelling the varia bles necessary to the mathematical analysis. The mechanical coupling connecting flywheel" and pendulum, for example, need not in a practical ous angle of roll.

embodiment be a belt transmission as shown. Referring to Figure 1, let 0 be the angle between the true vertical and a plane through thekeel of the ship normal to the deck; it is the instantaneu is the angle between the' pendulum and the vertical which it is our object to keep as nearly as possible equal to zero. 3 is the angle. of rotation of the flywheel relative to the true vertical. tween the flywheel and pendulum imposes a constant ratio R between the rotations of these two bodies relative to the ship so that The mechanical coupling bee lum about its axis of rotation to the algebraic sum of the torques acting about that axi There are three torques acting on the pendulum acting about the axis of rotation of the pendulum: v

(1) The gravitational restoring torquefiffizdiiqr (2) The torque due to the linear acceleration of the pendulum axis, caused by the shipsangw' lar motion:

In the diagram, for simplicity, the pendulum center is showndirectlyabove the ship center,-but that need not be so. But for satisfactory operation of the device at large angles of compensation the pendulumcenter has to be nearly vertically above the ships center of rotation. It will be understogd of course thatthe plane of pendulum oscillation is parallel to the plane of the ship oscillation which is to be compensated;

Thetorq-ue exerted by the flywheel on the pendulum results ina torque of reaction exerted by the pendulumon the flywheel equal to HR; so that the equation of motionof the flywheel'is L g3: FT dt (3) where; is the moment of inertia of the flywheel. Differentiating 1) twice with respect to time and substituting it into ('3) we obtain L"='RI R(&+ 4 thedoulole dot (such as indicates double diirerentiatiofn with respect to the time. Substituting this value of L into (2) and (3) V aeq e z a+mghe=( hmrr 12 1+ Rm) ('5 prog am inspection of Equation 5 it is clear thatif the coefficient or 5 vanishes, our purpose will be accomplished. The equation of motion of the system will be (drawin -"agile of a physical pendulum with a n unaccelerated pivot; It is to be noted, ho ever, that this equation shows that the period will tie v nae estates fer eenpeneeeea (vanishing er the cofiicient of 5) in Equation 5 is:

126 1-1b It is to be noted that com ensation cannot be obtained unless R is less than unity.

The moment of the pendulum, mh, will be determined in magnitude by the stabilizing function to be performed. The height H above the center of oscillation of the ship is fixed by the location where the stabilizer is required. Thus in order to minimize the requisite moment of inertiaiL which the flywheel must have, the expression R (1R') must be a maximum. This is accomplished by making R, equal to Thus the condition for compensation with minimum moment of inertia in the flywheel is expressed bythe two equations 4 hmH=I (9) If we insert these conditions into the equation ("7) for the period of the compensated pendulum We obtain showing that the compensated pendulum" has the period of a simple penumum of length S m-H rather than its much shorter equivalent length X. V

In the ideal casein which Equations 9 10 are e'iia'ctly satisfied this device will therefore perform two functions. gr) It eliminates any in: fluence' of purely rota'ry rollupon the action oithe' pendulum. (2) It changes the effective length of the p'endmum rromx to N+H, where His the height of the pivot above'the center or rotation of the boat, I D. Analysis of eperenea case of impeded compensation Inpractice Equation 9 cannot be satisfied precisely, principally owing to the fact that the height H of thependulum pivot above the center of rotation will not remaininvariant.

The equation of motion (5) of the system can be written as where I represents the fractional deviation from the balance condition (8). By fractional deviation from balance condition we mean the difference of the quantity hmH from the value IR(1'-R) required for ideal compensation, divided by the quantity hmH itself. Consider the following egample: let the quantity H (representing the height of the point of suspension above the axis of rotation of the ship) deviate from the value ,JR 1:-R) hm required by Equation 8 for perfect compensation. Let this deviation be designated by AH. This means ;IR(1-,R). H- AH Then by de fiination rauen .hmH 51 hmH H Hence in this case 6 simply represents AjH/I-I.

If the optimum ratio R is used, Equation 12 can be simplified to read sa+ a=Ha=AH 14 S k /h-FH=' \+H (15 is the equivalent pendulum length or the coinv 5: 20 Hence the difierential Equation 16 becomes:

Zi+w a= 6w5 005 mi Its solution is 6m a=mxd cos wt and hence we can obtain an expression tor the ratio between a and 0:

We thus obtain a direct expression for the compensation ratio attainable with this device.

Equation 17 assumes difierent forms in different frequency ranges:

Hence if the period of the system'exceeds the period of roll Equation 18, the compensation ratio simply approximates 6; ifthe period of roll exceeds the period of thesystem, (Equation 19) the compensation ratio equals 6 times the square of the ratio of the period of the system to .the period of the roll. In the resonant case,.Equation .20; the reduction ratio will materiallydep nd on damping. Let us consider a particular practical case ;For! a large ship the period is 10 seconds approximately. Consider the instrument to .be placed at a point on the deck such that the height of the axis of the pendulum above the center-of oscillation of the shipis 10 meters. Using :Equa tion 1'7, we obtain a 6 v 7152 g which is a satisfactory reduction-ratio Y E. Theory of damper to be used'w'ith the aperiodic stabilizer other hand, a certain amount of damping is 'necessary in order to cause a sufiiciently rapid. decay of the transient solution of the differential Equation 5; thus transient solutionrepresents the free. oscillation of a pendulum of length S=X+H (see Equation 11). i;- q '1:

A damping device in conjunction with the stabilizer must therefore fulfill therequirement that it does not give a rise to a damping force if the transient solution of Equation 5 is zero, but that it will contribute a damping term to the free oscillation of the system. This requirement can be fulfilled if damping of the pendulum is provided with respect to a neutral mass. Such a device could be constructed of two co-axial cylinders of radii r1 and r2; theouter one is linked to the pendulum, the inner one is freely rotating. Let the space between the cylinders be filled with liquid of coefficient of viscosity 1,. Let I be the moment of inertia of theinner cylinder and let A be the area of the cylinders. The operation of the device could be analyzed by setting up the differential equationof motion of the composite system and discussing its solution. Sucha procedure turns out to be excessively complex and hence a simplermethod of analysis is offered as follows: Take the optimum design condition for the damper to be the condition that the power delivered to the damper by the stabilizer shall be a maximum. Let the angular velocity of the outer cylinder be 101 and the angular velocity of the inner cylinder be 012. Let the'outer cylinder be driven such that w =A cos at=R[Ae (21) where a is the angular. frequency of the transient motion of the stabilizer? The notation R (complex quantity) heredenotes the real part of the complex quantity. In the following Equations '22 to 26 we shall use the complex exponentials in place of sinusoidal terms, it being implied that the real part only is meant to have physical reality. In Equation 2'7 and the following equations, the real part is then taken. This procedure is just'a mathematical expedient and can be shown to be fully justifiable. The equation of the motion of the inner wheel becomes:

' raA' Therefore the expression forthe'relative angular velocity between the members of'the damper becomes: a. a

r- I wg"'w =j I w I (26) Taking the real par t, as outlined. above: I

7 inner member; 'The' instentaneouspower is therefore giveil'byi If we put:

1c X Xe in: K2

This reduces 01 t This expression for the power loss in the damper assumes a maximum value for p l and the value of this maximum power is:

The condition p=1 is equivalent to:

*r1') 7 Al lg which is the design formula determining the viscosity of the medium in terms of the geometrical design parametersof the damper.

, It is of interest to note that for optimum adiius'tment the expression w2-@o1=i%' (34) gives the relation between the amplitudeof the relative angular velocity and of the driving angular velocity.

F. Theory of stabilizing torque produced ,by thestabilizing device,

In discussing the usefulness of the devi'cedescribed below, it is essential to have an expression for the stabilizing torque which the stabilizer provides toward the instrument to be stabilized.

The instrument to be stabilizedcan'zbe characterized by its effective momehtof inertia, elas-' tic or gravitational restoring torque, and frictional'to'rque. If the stabilizer is to be used with a given instrument, the effective moment of inertia and the restoring torque of the instrument can be included in the corresponding design parametersof the stabilizer, We are-therefore concerned only with. the effectoi an external Let the fric- -0=e0R(e (3'7) For solving the differential equation 36, we put:

a=aoe (38) This results in the solution:

Kjw0 mK +1e I w "K"w +m h (39) If the damping term JKw in the above expression can be considered. small relative to the other terms, we can simplify this expression into:

If the frequency of theship is considerably higher than thenatural frequency of the stabilizer, this expression can be further simplified to read:

This, by Equation 35, can be interpreted to mean:

L; maximum mgh Hence the'pendulum will swingthrough an angle whose crest value (expressed in radians) is the ratio of the maximum frictional torque (produced by the instrument to be stabilized) to the gravitational restoring torque of the pendulum.

'It is to be noted that the approximations made ifi'arriving'at Equation 42 are not'neeessary for the proper functioning of the device; their only purpose is to lead to a simplif ed expression which is valid'over the range of parameters where the approximations made are valid. If the approximations are not valid, thenthe accurate expression, Equation 39, must be used in computing the stabilization ratio attainable in the presence of a frictional torque;

G. Physical summary 07' the system A brief physical summary of the preceding analyses may be helpful to a clear understanding of the physical requirements of the apparatus.

The restoring or stabilizing power of the system depends solely on the product of h and m, the length and mass of the pendulum, which are chosen in view of the power desired; This power, given by my, then measures the restoring torque in-gravitational units per radian displacement of the system to be stabilized.

As has been stated, the coupling ratio between the pendulum andthe compensating neutral mass must be less than unity and is optimum at one-half. At that ratio the required compensating inertia is least; The ratio is not critical; smallvariations from the optimum are not greatly objectionable, but if the ratio approacheseither zero'or unity the nece'ssary value of the inertia becomes very large or approaches infinity.

With the pendulum length and mass chosen, and the coupling ratio adopted, the optimum compensating inertia then depends upon the height (H) of the pendulum center about the center of oscillation of the support -e-. g. of the ship (see Equation 8) Or, putting the matter in another way, for any given location relative to the oscillation center of the support, and assuming a couplingratio prefer-ably one-half, and specifying the'desired stabilizing power, the three quantities, pendulum length and mass, and compensating inertia, may then be muutually chosen to give maximum'compensation; And if adjustment is needed in any given installation to reach maximumcompensation, that adjustment may be of any, or all, the three quantities just named.

The-natural period'of the compensated system, as'stated, is the period of a pendulum having an equivalent length equal to that of the actual pendulumplus the height (H) of its center above the center of oscillation of the ship.

all cases,- the damping action is most effective when it'absorbspower at the maximum rate. The angular velocity of the driven member of the da'r'nperQWith' relation to the ship, must be equal to that of thependulum. These facts, and the explainedneutral quality, are the dampers only essentials;

- H} Actual device In the preceding. discussion the theory of a stabilizing device was described which essentially transforms a location at 'anarbitrar point on the'shipto a location at the ships center of oscillation. The perfection with which stabilization'can'be realized'islimited by (1) Linear accelerations of thecenter of oscillation of the boat. (2) Variations in the position of the center of oscillation. (3) Friction of the moving parts relative to the boat." It is believed that limitation (1) and (2) are not of a'serious'extent in the case of roll, but may seriously affect the satisfarctory operation of the device in the case of pitch. Theuse of-the device may therefore be limited to compensation of roll only. v

It is believed that the friction in the device and in the optical instruments to'be-stabilized can be reduced sufiiciently such that the error given by Equation 42 may be considered negligible.

The-device for one degree of freedom and with H 25x,- approximately, has been constructed, Fig-. ure 2, and found to function very satisfactorily; The stabilizer of Figure 2 consists of avertica'l member I8 mounted upon 'a base 2| which ordin'arily rests upon the deck 6. Approximately midway of vertical support member I8 horizontal arm I 4 is'pivoted at 20. l Arm l4 carries at its extremities inertia balls l3 and in proximity to its pivot 20-the working segments l2. From working segments l2 linkages 22' extend to cross beam 1 for supplying motion thereto. Cross beam 1 contains compensated pivot 8, uponwhich is hung pendulumllbyarmlfl. I

The damping means is composed of flywheel- |5-free---toturn upon ball bearings on pivot 16 inside a freely 'rotatablefluid filled case H which is-connected to cross-beam'l' by linkages 9. The

degree of the damping depends on the inertia of the flywheel and the' fluid viscosity. The op-' timu-rn damping is simply that which dissipated the maximum power in the fluid.

i; As a means of-testing thes'tabilizer the motion of-the ship was simulated by a motor driven pivoted beam-supporting device; w Stabilization was tested with an optical lever. The most severe test of the stabilizer occurs when the impressed frequency is close to the natural frequency of the system. In the test model the impressed period was about 1 second, while the natural period of the system was 2 seconds, Despite these conditions, more adverse than in practice, compensation to within /5 for a 60 swing of the support could easily be obtained. The condition for optimum compensation is completely independent of the period of the moving support. The balance condition (Equation 8) was found to be in agreement with theory.

The damper was adjusted for optimum operation; in this condition a 30 transient was reduced to less than within three full swings, Equation 34 determining the relative velocity of the two elements of the damper in optimum condition was verified.

I. Description of developed form Figures 3, 4, and 5 show a typical developed form of apparatus suitable for practical use. Here the .entire apparatus is housed and supported in a casing 20, of which one end 2| is hinged at 22 for ready access to the interior mechanism. In the present design the pendulum shaft 23 is provided with a dial 24 which may be observed through window 25 as a stabilization indicator. An instrument to be stabilized may be connected to that shaft. Or the disk, or the pendulum itself may be thought of as the instrument being stabilized. v

The pendulum shaft is mounted in bearing 26 in a supporting bracket 21 and in bearings 23 in a boss on the main supporting spider 29 which is-mounted directly in case 20. The pendulum (arm 30 and adjustable mass 3|) is mounted on shaft 23 directly behind case end 2| where it is accessible for length adjustment and/or change of mass. At the other end of shaft 23 a small sheave 32 takes a flexible metal belt 33 which runs over a larger sheave 34, the drive ratio being, preferably as stated, one-to-two. Sheave 34 is mounted on shaft 35 and overhangs the boss in which shaft bearings 36 are carried. The neutral compensating mass (I of the foregoing equations) is in the form of a metal annulus 31 mounted on shaft 35 via 'a supporting disk 38 and surrounding the bearing bosses.

The neutral damper mass is shown as preferably, although not necessarily, directly linked through viscous drag with the pendulum shaft 23. As shown here, it comprises fluid filled casing 40 rigidly mounted on a sleeve 4| which is rotatively locked to shaft 23. The neutral inertia mass of the damper is formed by a heavy annulus 42 .mounted. to rotate freely on bearings 43 on sleeve 4 Adjustments for maximum compensation can be made by shifting the pendulum mass on its arm. Larger adjustments can be made by substituting different masses 3|. And if it is desired to adjust the compensation without changing the restoring power of the pendulum, the inertia mass 31 may be adjusted. It may, for instance, be built up of a number of diskswhich may be placed and removed, so that its mass may be adjusted.- In the test device of Figure 2 the inertiamasses J3 on arm M are adjustable in. radius.:along the arm, as well as changeable, to adjust the inertia, .and the pendulum mass M is likewise adjustable on its arm Ill.

.To givev some illustrative figures, I may statev that the stabilizer .of' Figures 3,14, and 5 has beenv designed with a view to installations in which H may range from zero up to about thirty feet. An idea of physical dimensions may be had from the fact that compensating mass 3'! has mean diameter of 56 cm. (The figures are substantially to scale.) The pendulum mass and length, and the compensating mass, may be adjustably changed to give a wide variation in the restoring power and to adapt the instrument to variation of 1-1., But, assuming H to be 30 feet, and'assuming pendulum moment to be X 'gm.-cm., then the following figures result: '11) Restoring or stabilizing torque 5 10 gm.-cm., (2) Moment of inertia of mass 37=2 10 gm.-cm. (3) Weight of mass 37=25 10 g.-, (4) Mean diameter of mass 37:56 cm.

J. List of symbols used in specifications =angle of pendulum relative to ship. 0=angle between vertical and line normal to deck of ship.

u=angle between pendulum and vertical. p=angle of rotation of'com-pensating flywheel. 6o ao=crest values relative'to vertical of 0 and a. -R=transmission ratio. m=mass of pendulum. x=radius of gyration of pendulum. hz'distance fromc. o. g. to point of suspension of pendulum. I

\=equivalent length of simple pendulum to physical pendulum.

' H=distance from pcintof suspension of pendulum to center of rotation 'of-ship.

L=torque produced by flywheel on pendulum. g=acceleration of gravity. I=moment of inertia or flywheel. S=length of simple pendulum equivalent to composite system.

a=fractional deviation from -idea1 compensation.

wo=natural angular frequency of compound system.

w=angular frequencypf ship. r1=radius of outer member "of damper. rz=radius of inner member of damper.

=coefficient of viscosity-of damping fluid. 7C:1;A'ri /'(T2'r1) w1=angular "velocity of outer -me'mber of damper.

oz=angular "velocity of inner member of damper. V

I=moment 'of inertiagof inner "member of damper.

' a angular frequency'of transient.

lia -external frictional torque "on compensator.

K=frictional torque per unitrelative angular velocity.

A=contact area of damper.

A=amplitude of'angular velo'city'of outer member of damper.

[ l=absolute value-of RE l--real part "of I claim:

1. In a stabilizer .for compensating for oscillations of a support about an effective 'center,..a compensated pendulum system, comprising a pendulum pivoted for gravitational oscillation at a pivot point removed from the efiective center of support oscillation by a distance'havinga predetermined normally vertical component .(H'), a freely rotatable compensating mass of .-prede-.

termined moment of inertia (1);, about its rota-- tional axis mounted in neutral equilibrium about. that axis On the oscillating support, and .movement transmitting connection between the pendulum and inertia mass such that the ratio (R) of angular velocity-of the latter to that of the former is less than unity.

2. A stabilizer as specified in claim 1, and in which the stated angular velocity ratio is approximately one-half. q

3. A stabilizer as specified'inclaim .1, andin which the moment of inertia '(I') of the compensating mass is substantially defined by the damping means having one member connectedto oscillate with the compensated pendulum system.

6. A stabilizer as specified vinclaim 1, and in which the inertia (I) of the compensating amass is substantially defined by the :iormula,

where h and m are, respectively, the lengthand;

mass .of thependulum, and where the ratio IR approximately one-half, land the stabilizer also including a .neutral power dissipative damping means having one'memberconnected to oscillate with the compensated pendulum .esys'tem.

7. .A stabilizer of .the type herein described, comprising a frame, .a pendulum shaft and -an inertiamass shaft .journalled in the. frame, rotation transmitting connection between the two shafts such thatthe ratio of angular velocity .of the lattertothat of .the former is less than unity, a pendulum suspended from thependulum. shaft, an inertia .mass .mounted .in .neutralequilibrium on theinertia mass.s'haift,.and a neutral damping means mounted inneutral equilibrium-phone ofthe shafts.

8. .A stabilizer asspecified in .claim L-and-in which thellength and mass offthe vpendulumand the moment of inertia of the inertia mass are adjustable.

9. A stabilizer asspecifiedin claim Land which the neutral-damping means is mounted directly on the pendulum shaft. Y I

10. A stabilizer of-thetype herein described, comprising a frame, a-pendu'lumrshaftand ean inertia .mass shaft iournalled in the frame parallel to each other, rotation transnii-ttingeconnection between the .two shattssuch that the ratio of angular velocity of the tlatter e 1 that'iof the former is approximately one-yhalf n pendulum suspended irom the pendulumshaf-t, aninertia mass mountedin neutraleequilibrium;.omthe inertia mass shaft,a neutral .damp ngvmeans comprising two concentrically rotatable members with a dani-ping fluidnbetween athem, tone of said members .being;edirectly-imountedroni and rotating 'with the pendulum shaft, the -.-relati ons of the several parts :being-.determinedapproxi-z mately-by thev formula, 4% 1 .R =(I)-=hmH;, where Ris the ratio stated :above,.--L-is the inertia mo ment :of the inertia lmassifh andgmaarfi, N59 C-- former to that of the latter is approximately onehalf, and adjusting the moment of inertia (I) of the inertia mass to substantially the value expressed by, R(1R) (I) =hmH, where h and m are, respectively, the length and mass of the pendulum.

WOLFGANG K. H. PANOFSKY.

lie references cited. 

